Related papers: Money as Minimal Complexity
For a closed orientable connected 3-manifold $M$, its complexity $\boldsymbol{T}(M)$ is defined to be the minimal number of tetrahedra in its triangulations. Under the assumption that $M$ is prime (but not necessarily atoroidal), we…
Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such…
Given a graph $G=(V,E)$ with $V=\{1,\ldots,n\}$, we place on every vertex a token $T_1,\ldots,T_n$. A swap is an exchange of tokens on adjacent vertices. We consider the algorithmic question of finding a shortest sequence of swaps such that…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…
Over the past five decades a number of multilateral index number systems have been proposed for spatial and cross-country price comparisons. These multilateral indexes are usually expressed as solutions to systems of linear or nonlinear…
It is observed that in some money exchange operations, the applied $n$ -variable mean $M$ should be self reciprocally-conjugate, i.e. it should satisfy the equality \[ M\left( x_{1},\ldots,x_{n}\right) M\left(…
We study the computational complexity of fairly allocating indivisible, mixed-manna items. For basic measures of fairness, this problem is hard in general. Thus, research has flourished concerning input classes where efficient algorithms…
The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in…
We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The…
Maximizing the revenue from selling two or more goods has been shown to require the use of $nonmonotonic$ mechanisms, where a higher-valuation buyer may pay less than a lower-valuation one. Here we show that the restriction to $monotonic$…
The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and…
We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism for this problem that maintains a balanced budget. We…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer's valuations within a set of distributions, called an "ambiguity" set. We identify the exact forms of…
We propose a simple market model where agents trade different types of products with each other by using money, relying only on local information. Value fluctuations of single products, combined with the condition of maximum profit in…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
A new electronic structure principle, viz. the minimum magnetizability principle (MMP) has been proposed and also has been verified through ab initio calculations, to extend the domain of applicability of the conceptual density functional…
We consider the {\em MST-interdiction} problem: given a multigraph $G = (V, E)$, edge weights $\{w_e\geq 0\}_{e \in E}$, interdiction costs $\{c_e\geq 0\}_{e \in E}$, and an interdiction budget $B\geq 0$, the goal is to remove a set…
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly…